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Category: Differentiation

y-x-x-x-dy-dx-

Question Number 179258 by zaheen last updated on 27/Oct/22 $${y}={x}^{{x}^{{x}} } \\ $$$$\frac{{dy}}{{dx}}=? \\ $$ Commented by CElcedricjunior last updated on 30/Oct/22 $$\left.{y}=\boldsymbol{\mathrm{x}}^{\boldsymbol{\mathrm{x}}^{\boldsymbol{\mathrm{x}}} } =\boldsymbol{\mathrm{e}}^{\boldsymbol{\mathrm{x}}^{\boldsymbol{\mathrm{x}}}…

a-2-x-2-y-2-b-2-x-2-y-2-a-b-2x-2-x-4-x-4-y-2-Find-x-such-that-y-is-minimum-Assume-x-y-gt-0-

Question Number 48118 by ajfour last updated on 19/Nov/18 $$\sqrt{{a}^{\mathrm{2}} {x}^{\mathrm{2}} −{y}^{\mathrm{2}} }+\sqrt{{b}^{\mathrm{2}} {x}^{\mathrm{2}} −{y}^{\mathrm{2}} } \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:=\:\left({a}+{b}\right)\sqrt{\mathrm{2}{x}^{\mathrm{2}} +\frac{{x}^{\mathrm{4}} }{{x}^{\mathrm{4}} −{y}^{\mathrm{2}} }} \\ $$$${Find}\:{x}\:{such}\:{that}\:{y}\:{is}\:{minimum}. \\…

y-2ay-1-a-2-y-te-at-sint-

Question Number 113444 by Ar Brandon last updated on 13/Sep/20 $$\mathrm{y}''−\mathrm{2ay}'+\left(\mathrm{1}+\mathrm{a}^{\mathrm{2}} \right)\mathrm{y}=\mathrm{te}^{\mathrm{at}} +\mathrm{sint} \\ $$ Answered by Ar Brandon last updated on 13/Sep/20 $$\mathrm{y}''−\mathrm{2ay}'+\left(\mathrm{1}+\mathrm{a}^{\mathrm{2}} \right)\mathrm{y}=\mathrm{te}^{\mathrm{at}}…

y-sinh-1-sin-x-dy-dx-

Question Number 113196 by bobhans last updated on 11/Sep/20 $$\:\mathrm{y}\:=\:\mathrm{sinh}\:^{−\mathrm{1}} \left(\mathrm{sin}\:\mathrm{x}\right)\:,\:\frac{\mathrm{dy}}{\mathrm{dx}}\:=? \\ $$ Answered by MJS_new last updated on 11/Sep/20 $$\left({f}\left({g}\left({x}\right)\right)'={g}'\left({x}\right)×{f}'\left({g}\left({x}\right)\right)\right. \\ $$$$\left(\mathrm{sinh}^{−\mathrm{1}} \:\mathrm{sin}\:{x}\right)'=\mathrm{cos}\:{x}\:×\frac{\mathrm{1}}{\:\sqrt{\mathrm{1}+\mathrm{sin}^{\mathrm{2}} \:{x}}}…

Corona-virus-covid-19-is-spreading-through-a-certain-country-Let-the-constant-S-be-the-number-of-people-susceptible-to-infection-The-infection-rate-is-proportional-to-the-the-product-of-the-alre

Question Number 178682 by MikeH last updated on 20/Oct/22 $$\mathrm{Corona}\:\mathrm{virus}\:\left(\mathrm{covid}\:−\mathrm{19}\right)\:\mathrm{is}\:\mathrm{spreading}\:\mathrm{through}\:\mathrm{a} \\ $$$$\mathrm{certain}\:\mathrm{country}.\:\mathrm{Let}\:\mathrm{the}\:\mathrm{constant}\:{S}\:\mathrm{be}\:\mathrm{the}\:\mathrm{number} \\ $$$$\mathrm{of}\:\mathrm{people}\:\mathrm{susceptible}\:\mathrm{to}\:\mathrm{infection}.\:\:\mathrm{The}\:\mathrm{infection}\:\mathrm{rate} \\ $$$$\mathrm{is}\:\mathrm{proportional}\:\mathrm{to}\:\mathrm{the}\:\mathrm{the}\:\mathrm{product}\:\mathrm{of}\:\mathrm{the}\:\mathrm{already} \\ $$$$\mathrm{infected}\:\mathrm{people}\:\left({x}\right)\:\mathrm{and}\:\mathrm{the}\:\mathrm{number}\:\mathrm{of}\:\mathrm{susceptible}\:\mathrm{but}\: \\ $$$$\mathrm{but}\:\mathrm{uninfected}\:\mathrm{people}\:\left({S}−{x}\right).\:\mathrm{establish}\:\mathrm{the}\: \\ $$$$\mathrm{differential}\:\mathrm{equation}. \\ $$ Terms…

400-2-100-2-

Question Number 47532 by 143jesus last updated on 11/Nov/18 $$\sqrt{\mathrm{400}^{\mathrm{2}} +\mathrm{100}^{\mathrm{2}=} } \\ $$ Answered by Joel578 last updated on 11/Nov/18 $$=\:\sqrt{\mathrm{160000}\:+\:\mathrm{10000}}\:=\:\sqrt{\mathrm{170000}}\:=\:\mathrm{100}\sqrt{\mathrm{17}}\:\approx\:\mathrm{412}.\mathrm{31} \\ $$ Answered…